Model for random internalization of nanoparticles by cells.

We propose a stochastic model for the internalization of nanoparticles by cells formulating cellular uptake as a compound Poisson process with a random probability of success. This is an alternative approach to the one presented by Rees et al. [Nat.

Engulfment and Pushing of Cylindrical Liquid Nano-Inclusion by Advancing Crystal/Melt Interface: An Atomistic Simulation Study.

We reported a molecular dynamics (MD) simulation study of an advancing pure Al(100)/melt interface that encounters a foreign immiscible liquid Pb cylindrical nano-inclusion. When the advancing interface approaches the inclusion, the interface may engulf, push to an extent and then engulf or push the nano-inclusion away from the solidifying phase depending on the velocity of the interface. Here, we investigated cylindrical liquid Pb nano-inclusion pushing or engulfment by a growing crystal Al that strongly depends on the velocity of the crystal/melt interface, and a critical velocity (vc) is deduced.

The role of incoming flow on crystallization of undercooled liquids with a two-phase layer.

Motivated by important applications of crystallization phenomena, we consider a directional solidification process for a binary melt with a two-phase (mushy) layer in the presence of weak melt flow. We consider the steady-state solidification scenario, so that the two-phase layer filled with solid and liquid material keeps its thickness. In addition, we consider that the melt flows onto the two-phase layer slowly in the opposite direction to directional crystallization and solidifies there.

Dynamical law of the phase interface motion in the presence of crystals nucleation.

In this paper, we develop a theory of solid/liquid phase interface motion into an undercooled melt in the presence of nucleation and growth of crystals. A set of integrodifferential kinetic, heat and mass transfer equations is analytically solved in the two-phase and liquid layers divided by the moving phase transition interface. To do this, we have used the saddle-point method to evaluate a Laplace-type integral and the small parameter method to find the law of phase interface motion.

Modelling of hemodynamics in bifurcation lesions of coronary arteries before and after myocardial revascularization.

Modelling of patient-specific hemodynamics for a clinical case of severe coronary artery disease with the bifurcation stenosis was carried out with allowance for standard angiographic data obtained before and after successfully performed myocardial revascularization by stenting of two arteries. Based on a non-Newtonian fluid model and an original algorithm for fluid dynamics computation operated with a limited amount of initial data, key characteristics of blood flow were determined to analyse the features of coronary disease and the consequences of its treatment. The results of hemodynamic modelling near bifurcation sites are presented with an emphasis on physical, physiological and clinical phenomena to demonstrate the feasibility of the proposed approach.

Transport phenomena in complex systems (part 2).

This theme issue, in two parts, continues research studies of transport phenomena in complex media published in the first part (Alexandrov & Zubarev 2021 , 20200301. (doi:10.1098/rsta.

Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids.

When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered.

The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid.

This manuscript is concerned with the theory of nucleation and evolution of a polydisperse ensemble of crystals in metastable liquids during the intermediate stage of a phase transformation process. A generalized growth rate of individual crystals is obtained with allowance for the effects of their non-stationary evolution in unsteady temperature (solute concentration) field and the phase transition temperature shift appearing due to the particle curvature (the Gibbs-Thomson effect) and atomic kinetics. A complete system of balance and kinetic equations determining the transient behaviour of the metastability degree and the particle-radius distribution function is analytically solved in a parametric form.

Ostwald ripening in the presence of simultaneous occurrence of various mass transfer mechanisms: an extension of the Lifshitz-Slyozov theory.

The Ostwald ripening stage of a phase transformation process with allowance for synchronous operation of various mass transfer mechanisms (volume diffusion and diffusion along the block boundaries and dislocations) and the initial condition for the particle-radius distribution function is theoretically studied. The initial condition is taken from the analytical solution describing the intermediate stage of a phase transition process. The present theory focuses on relaxation dynamics from the beginning of the ripening process to its final asymptotic state, which is described by the previously constructed theories (Slezov VV.

Transport phenomena in complex systems (part 1).

The issue, in two parts, is devoted to theoretical, computational and experimental studies of transport phenomena in various complex systems (in porous and composite media; systems with physical and chemical reactions and phase and structural transformations; in biological tissues and materials). Various types of these phenomena (heat and mass transfer; hydrodynamic and rheological effects; electromagnetic field propagation) are considered. Anomalous, relaxation and nonlinear transport, as well as transport induced by the impact of external fields and noise, is the focus of this issue.

A review on the theory of stable dendritic growth.

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented.

The shape of dendritic tips: a test of theory with computations and experiments.

This article is devoted to the study of the tip shape of dendritic crystals grown from a supercooled liquid. The recently developed theory (Alexandrov & Galenko 2020 , 20190243. (doi:10.

Evaporation kinetics of a polydisperse ensemble of drops.

A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear 'diffusion' term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g.

Anomalous climate dynamics induced by multiplicative and additive noises.

Anomalous behavior of a nonlinear climate-vegetation model governed by the multiplicative and additive noises is revealed on the basis of stochastic sensitivity analysis. A specific feature of this model is the bistability with the coexistence of "snowball" equilibrium and "warm" attractor in the form of equilibrium or cycle. It is found that multiplicative and additive noises shift probabilistic distribution in opposite directions.

Dissolution of polydisperse ensembles of crystals in channels with a forced flow.

A non-stationary integro-differential model describing the dissolution of polydisperse ensembles of crystals in channels filled with flowing liquid is analysed. The particle-size distribution function, the particle flux through an arbitrary cross-section of the channel, the particle concentration profile, as well as the disappearance intensity of particles are found analytically. It is shown that a nonlinear behaviour of solutions is completely defined by the source term of particles introduced into the channel.

From nucleation and coarsening to coalescence in metastable liquids.

The transition of a metastable liquid (supersaturated solution or supercooled melt) occurring from the intermediate stage (where the crystals nucleate and grow) to the concluding stage (where the larger particles evolve at the expense of the dissolution of smaller particles) is theoretically described, with allowance for various mass transfer mechanisms (reaction on the interface surface, volume diffusion, grain-boundary diffusion, diffusion along the dislocations) arising at the stage of Ostwald ripening (coalescence). The initial distribution function (its 'tail') for the concluding stage (forming as a result of the evolution of a particulate assemblage during the intermediate stage) is taken into account to determine the particle-size distribution function at the stage of Ostwald ripening. This modified distribution function essentially differs from the universal Lifshitz-Slyozov (LS) solutions for several mass transfer mechanisms.

Patterns in soft and biological matters.

The issue is devoted to theoretical, computer and experimental studies of internal heterogeneous patterns, their morphology and evolution in various soft physical systems-organic and inorganic materials (e.g. alloys, polymers, cell cultures, biological tissues as well as metastable and composite materials).

Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics.

This manuscript is devoted to the nonlinear dynamics of particulate assemblages in metastable liquids, caused by various dynamical laws of crystal growth and nucleation kinetics. First of all, we compare the quasi-steady-state and unsteady-state growth rates of spherical crystals in supercooled and supersaturated liquids. It is demonstrated that the unsteady-state rates transform to the steady-state ones in a limiting case of fine particles.

The shape of dendritic tips.

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number.

The effect of density changes on crystallization with a mushy layer.

A nonlinear problem with two moving boundaries of the phase transition, which describes the process of directional crystallization in the presence of a quasi-equilibrium two-phase layer, is solved analytically for the steady-state process. The exact analytical solution in a two-phase layer is found in a parametric form (the solid phase fraction plays the role of this parameter) with allowance for possible changes in the density of the liquid phase accordingly to a linearized equation of state and arbitrary value of the solid fraction at the boundary between the two-phase and solid layers. Namely, the solute concentration, temperature, solid fraction in the mushy layer, liquid and solid phases, mushy layer thickness and its velocity are found analytically.

Phase transformations in metastable liquids combined with polymerization.

This paper is concerned with the theory of nucleation and growth of crystals in a metastable polymer melt with allowance for the polymerization of a monomer. A mathematical model consisting of the heat balance equation, equations governing the particle-radius distribution function and the polymerization degree is formulated. The exact steady-state analytical solutions are found.

Diffusionless (chemically partitionless) crystallization and subsequent decomposition of supersaturated solid solutions in Sn-Bi eutectic alloy.

Results of a study on microstructural evolution of eutectic Sn-57 wt.% Bi processed with cooling rates of 10, 1 K s and approximately 10 K s are presented. In order to distinguish different mechanisms of microstructure formation, a comparison with microstructures of different hypoeutectic alloys with compositions down to below the maximum solubility of Bi in Sn-Bi is undertaken.

On the theory of crystal growth in metastable systems with biomedical applications: protein and insulin crystallization.

A generalized theory of nucleation and growth of crystals in a metastable (supercooled or supersaturated) liquid is developed taking into account two principal effects: the diffusion mechanism of the particle-size distribution function in the space of particle radii and the unsteady-state growth rates of individual crystals induced by fluctuations in external temperature or concentration field. A system of the Fokker-Planck and balance integro-differential equations is formulated and analytically solved in a parametric form for arbitrary nucleation kinetics and arbitrary growth rates of individual crystals. The particle-size distribution function and system metastability are found in an explicit form.

On the theory of the unsteady-state growth of spherical crystals in metastable liquids.

Motivated by a large number of applications, we consider the process of non-stationary growth of spherical crystals in a supercooled binary melt. The moving-boundary problem describing the unsteady-state distributions of temperature and impurity concentration around the growing crystal as well as the dynamics of its radius and growth rate is solved by means of the methods of small-parameter expansion and Laplace-Carson integral transform. We show that the growth rate of crystals contains the main contribution (which is proportional to the supercooling degree Δ) and the first correction (which is proportional to Δ t, where t is time).

Heterogeneous materials: metastable and non-ergodic internal structures.

This issue is concerned with structural and phase transitions in heterogeneous and composite materials, the effects of external magnetic fields on these phenomena and the macroscopic properties and behaviour of materials with isotropic and anisotropic internal structures. Using experimental, theoretical and computer methods, these transitions are studied at the atomic and mesoscopic levels. The fundamental specific feature of structural transitions in many heterogeneous media consists of the fact that these transitions are stacked for a long time in non-equilibrium states that appear due to either macroscopic dissipative processes (an alternating magnetic field or hydrodynamic flow, for instance) or system lifetime in a metastable state.